The first component is the `Semantic Alignment Network' (SAN), which consist of an adjustable FC layer, whose parameters are denoted as \(\mathbf {W}_1 \in \mathbb {R}^{d\times d}\) , that projects the input visual feature vectors to a semantic space with \(d\)  dimensions. The resulting feature maps are then projected onto the fixed semantic embeddings, denoted by \(\mathbf {W}_2 \in \mathbb {R}^{d \times (\mathrm {C}+1)}\) , which are obtained in an unsupervised manner by text mining (e.g., Word2vec and GloVe embeddings). Note that, here we consider both seen and unseen semantic vectors which require unseen classes to be predefined. This consideration is inline with a very recent effort [1]} which adopt this setting to explore the cluster manifold structure of the semantic embedding space and address domain shift issue.
Given a feature representation input to SAN in the top branch, \(\mathbf {f}^t\) , the overall operation can be represented as:
\(\mathbf {o} = (\mathbf {W_1}\mathbf {W_2})^T \mathbf {f}^t.\) 
